Details

sample230.0ms

Algorithm

intervals

Results

73.0ms	39×	body	640	valid
70.0ms	276×	body	80	valid
36.0ms	26×	body	1280	valid
13.0ms	17×	body	320	valid
7.0ms	15×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
6	5437
5	1878
4	761
3	231
2	72
1	34
0	17

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
3.2b	(cos (/ (+ phi2 phi1) 2))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-l`
7×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

12.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
37.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
15.0ms	(cos (/ (+ phi2 phi1) 2))

series862.0ms

Counts

3 → 9

Calls

3 calls:

687.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
133.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
42.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.1s

Counts

65 → 65

Iterations

Iter	Nodes
3	3356
2	915
1	307
0	128

prune815.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
0.2b	(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
0.5b	(log1p (cos (/ (+ phi2 phi1) 2)))
3.2b	(cos (/ (+ phi2 phi1) 2))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`expm1-log1p-u` `associate-l`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/`
1×	`log1p-udef` `expm1-log1p` `flip3--` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `expm1-udef` `difference-of-squares` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

30.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
0.0ms	(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
1.0ms	(log1p (cos (/ (+ phi2 phi1) 2)))
14.0ms	(cos (/ (+ phi2 phi1) 2))

series322.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
64.0ms	(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
61.0ms	(log1p (cos (/ (+ phi2 phi1) 2)))
25.0ms	(cos (/ (+ phi2 phi1) 2))

simplify3.2s

Counts

71 → 71

Iterations

Iter	Nodes
4	4942
3	1381
2	475
1	205
0	101

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))
3.2b	(cos (/ (+ phi1 phi2) 2))
3.2b	(cos (/ (+ phi1 phi2) 2))
3.2b	(cos (/ (+ phi1 phi2) 2))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 44

Calls

4 calls:

29.0ms	(cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))
8.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))

series116.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))
23.0ms	(cos (/ (+ phi1 phi2) 2))
33.0ms	(cos (/ (+ phi1 phi2) 2))
24.0ms	(cos (/ (+ phi1 phi2) 2))

simplify3.0s

Counts

56 → 56

Iterations

Iter	Nodes
9	3837
8	1744
7	1106
6	813
5	656
4	436
3	212
2	117
1	77
0	48

prune995.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.1b

localize68.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (/ (+ phi1 phi2) 2))
3.2b	(cos (/ (+ phi1 phi2) 2))
3.2b	(cos (/ (+ phi1 phi2) 2))
3.2b	(cos (/ (+ phi1 phi2) 2))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 40

Calls

4 calls:

22.0ms	(cos (/ (+ phi1 phi2) 2))
17.0ms	(cos (/ (+ phi1 phi2) 2))
12.0ms	(cos (/ (+ phi1 phi2) 2))
9.0ms	(cos (/ (+ phi1 phi2) 2))

series131.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cos (/ (+ phi1 phi2) 2))
33.0ms	(cos (/ (+ phi1 phi2) 2))
36.0ms	(cos (/ (+ phi1 phi2) 2))
38.0ms	(cos (/ (+ phi1 phi2) 2))

simplify1.5s

Counts

52 → 52

Iterations

Iter	Nodes
9	2126
8	1072
7	742
6	537
5	424
4	299
3	152
2	83
1	54
0	28

prune1.1s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 3.1b

regimes936.0ms

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.6s	8311×	body	80	valid
1.8s	1306×	body	640	valid
1.2s	786×	body	1280	valid
643.0ms	705×	body	320	valid
193.0ms	377×	body	160	valid